*t*test is used when two sets of values are related, for example because each of a pair of measurements was made on the same subject.

In this case, it is the mean of the difference between the two values that is distributed according to the t distribution.

This example is from Dalgard.

Not only are the values correlated, but the difference is always negative:

We can do the test by hand, as follows:

The question now is, what fraction of the values from the t-distribution with df = 10 are greater than 11.39?

The short answer: not very many!

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